As Dimitri ans bhargav said, this is automatic for categories with internal homs. And you don't need x to be the product: you have the same result for any closed monoidal category (in your case it is cartesian closed). You can find it in "Basic concepts of enriched category theory", by G.M. Kelly, page 14, which you can get for free here: http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html .